Author here. Thanks for the appreciation!
Since this piece was written, I have discovered another notation by John Tromp which I consider to be the most breathtakingly beautiful:
- https://tromp.github.io/cl/diagrams.html
Here used by Paul Crowley to describe Graham's number:
- https://mindsarentmagic.org/2020/02/19/a-picture-of-grahams-...
- https://mindsarentmagic.org/2020/02/24/some-more-numbers-as-...